Reduction algorithms are an important tool for understanding structural properties of groups. They play an important role in algorithms designed to investigate matrix groups over a finite field. One such algorithm was designed by Brooksbank et al. for members of the class $C_6$ in Aschbacher's theorem, namely groups $N$ that are normalizers in $GL(d,q)$ of certain absolutely irreducible symplectic-type $r$-groups $R$, where $r$ is a prime and $d=r^n$ with $n>2$. However, the analysis of this algorithm has only been completed when $d=r^2$ and when $d=r^n$ and $n>2$, in the latter case under the condition that $G/RZ(G)\cong N/RZ(N)$. We prove that the algorithm runs successfully for some groups in the case of $d=r^3$ without any assumption.
ÇAĞMAN, ABDULLAH and ANKARALIOĞLU, NURULLAH
"A contribution to the analysis of a reduction algorithm for groups with an extraspecial normal subgroup,"
Turkish Journal of Mathematics: Vol. 40:
4, Article 20.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss4/20